docs: fix cherry-pick duplicate 9d/9e sections — merge into unified structure

Auto-merge from cherry-pick concatenated both branch versions of Phase 9d
and 9e. This commit resolves the duplication:

- 9d now has 4 sub-items (9d.1–9d.4) combining both branches:
    9d.1  ConesUtility (detailed: BFS, auto-placement, quantization)
          + Troyanov/Springborn refs (from literature analysis)
    9d.2  Non-Euclidean cone extensions (RESEARCH)
          + Bobenko-Lutz 2025 + Crane 2018 (from literature analysis)
    9d.3  StereographicUnwrapper + SphereUtility
    9d.4  MobiusCenteringFunctional
- 9e keeps the detailed reviewer/meeting-prep version
  + adds mathematical references (Bobenko-Hoffmann-Springborn 2006)
- 9f (Polygon Laplacian, Alexa 2011/2020) retained as standalone section

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

doc/roadmap/phases.md

@@ -129,16 +129,22 @@ mesh type.
                              + holonomy infrastructure.
          Effort: ~2 weeks for fundamental polygon, +2 weeks for surgery
                  layer, +1 week integration.
+```
 
-9d — Cone singularities + sphere atlas  (Java port + research extension)
+9d — Cone metrics + sphere utilities  (Java port + research extension)
-────────────────────────────────────────────────────────────────────────
+────────────────────────────────────────────────────────────────────
 
-9d.1   ConesUtility  (Java port — Euclidean only)
+```
-         → cones_utility.hpp
+9d.1   ConesUtility  (Java port: unwrapper/ConesUtility.java)
-         Java source: ConesUtility.java  (~200 lines)
+         → cone_singularities.hpp
+         Fills the "⚠️ data structure only" gap in java-parity.md:
+         - Detect interior cone vertices (angle deficit ≠ 0)
+         - BFS path from cone to mesh boundary → cut edge set
+         - Auto-placement: conjugate gradient on Θ-gradient magnitude
+         - Quantization: snap cone angles to π/2, π/3, π/6 for
+           quad / triangle / hexagonal atlas targets
+         Java reference: unwrapper/ConesUtility.java
          Mathematical reference: Troyanov 1991 + Springborn 2020 §3
-         Port scope: prescribed cone angles Θᵥ ≠ 2π in Euclidean mode.
-         Status: 🔲 planned
 
 9d.2   Non-Euclidean cone extensions  (RESEARCH, not in Java)
          → extend ConesUtility to HyperIdeal + Spherical modes
@@ -153,68 +159,13 @@ mesh type.
              automatic cone placement; directly applicable to 9d.2 algorithm.
          Status: 🔲 planned
 
-9d.3   StereographicUnwrapper  (Java port)
+9d.3   StereographicUnwrapper + SphereUtility  (Java port)
-         → stereo_unwrapper.hpp
-         Java source: StereographicUnwrapper.java (266 lines)
-         Converts spherical DCE output (Point_3 on S²) to a 2-D atlas
-         via stereographic projection + Möbius centring.
-         Closes the visualisation gap from discrete_conformal_map_spherical().
-         Effort: small (~3 days).
-         Status: 🔲 planned
-
-9e — CirclePatternLayout  (Java port)
-─────────────────────────────────────
-
-9e     CirclePatternLayout + CirclePatternUtility  (Java port)
-         → circle_pattern_layout.hpp
-         Java sources: CirclePatternLayout.java + CirclePatternUtility.java
-                       + CPEuclideanRotation.java
-         Mathematical reference: Bobenko-Springborn 2004 variational principle
-                                 + Bobenko-Hoffmann-Springborn 2006 "Minimal
-                                   surfaces from circle patterns" (Discrete &
-                                   Comput. Geom. 35, 2006).
-         Status: 🔲 planned
-
-9f — Polygon Laplacian  (RESEARCH — no Java equivalent)
-──────────────────────────────────────────────────────
-
-9f     Discrete Laplacian on general polygonal meshes
-         → polygon_laplacian.hpp
-         Java source: NONE
-         Mathematical reference:
-           Alexa, Wardetzky 2011 "Discrete Laplacians on General Polygonal
-             Meshes" (ACM SIGGRAPH 2011) — virtual-node construction,
-             polygon cotangent weights extending the Pinkall-Polthier formula.
-           Alexa 2020 "Discrete Laplacians on General Polygonal Meshes"
-             (ACM TOG 39, 2020) — extended journal treatment, error bounds.
-         Enables: DCE energy evaluation on quad-dominant / Voronoi /
-                  polygon meshes without forced triangulation.
-                  Replaces euclidean_hessian.hpp for non-triangular inputs.
-         Status: 🔲 planned (pure research, no Java source)
-         Effort: medium (~2 weeks core + tests; +1 week Newton integration).
-```
-
-9d — Cone metrics + sphere utilities  (Java port — 2026 library scan)
-────────────────────────────────────────────────────────────────────
-
-```
-9d.1   ConesUtility  (Java port: unwrapper/ConesUtility.java)
-         → cone_singularities.hpp
-         Fills the "⚠️ data structure only" gap in java-parity.md:
-         - Detect interior cone vertices (angle deficit ≠ 0)
-         - BFS path from cone to mesh boundary → cut edge set
-         - Auto-placement: conjugate gradient on Θ-gradient magnitude
-         - Quantization: snap cone angles to π/2, π/3, π/6 for
-           quad / triangle / hexagonal atlas targets
-         Java reference: unwrapper/ConesUtility.java
-
-9d.2   StereographicUnwrapper + SphereUtility  (Java port)
          → stereographic_layout.hpp
          Stereographic projection S²→ℂ∪{∞} + Möbius centering for
          genus-0 surfaces. Converts spherical DCE output to a flat 2-D atlas.
          Java reference: unwrapper/StereographicUnwrapper.java (266 lines)
 
-9d.3   MobiusCenteringFunctional  (Java port, optional upgrade)
+9d.4   MobiusCenteringFunctional  (Java port, optional upgrade)
          → integrate into layout.hpp normalise_hyperbolic()
          Variational Möbius centering via Lorentz geometry:
            E = Σ log(-⟨x,p⟩/√(-⟨x,x⟩))
@@ -235,6 +186,30 @@ mesh type.
          - CPEuclideanRotation: rotation-invariant CP functional variant
          Java references: unwrapper/circlepattern/CirclePattern{Layout,Utility}.java
                           unwrapper/circlepattern/CPEuclideanRotation.java
+         Mathematical reference: Bobenko-Springborn 2004 variational principle
+                                 + Bobenko-Hoffmann-Springborn 2006 "Minimal
+                                   surfaces from circle patterns" (Discrete &
+                                   Comput. Geom. 35, 2006).
+```
+
+9f — Polygon Laplacian  (RESEARCH — no Java equivalent)
+──────────────────────────────────────────────────────
+
+```
+9f     Discrete Laplacian on general polygonal meshes
+         → polygon_laplacian.hpp
+         Java source: NONE
+         Mathematical reference:
+           Alexa, Wardetzky 2011 "Discrete Laplacians on General Polygonal
+             Meshes" (ACM SIGGRAPH 2011) — virtual-node construction,
+             polygon cotangent weights extending the Pinkall-Polthier formula.
+           Alexa 2020 "Discrete Laplacians on General Polygonal Meshes"
+             (ACM TOG 39, 2020) — extended journal treatment, error bounds.
+         Enables: DCE energy evaluation on quad-dominant / Voronoi /
+                  polygon meshes without forced triangulation.
+                  Replaces euclidean_hessian.hpp for non-triangular inputs.
+         Status: 🔲 planned (pure research, no Java source)
+         Effort: medium (~2 weeks core + tests; +1 week Newton integration).
 ```
 
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